Abstract: It has recently become experimentally possible to monitor the energy levels of a superconducting transmon qubit continuously in time using microwave fields. Such measurements weakly perturb the qubit per unit time, lead to a competition between unitary Hamiltonian dynamics and non-unitary collapse dynamics. I review several subtleties about modeling this measurement process, and discuss several recent achievements made in collaboration with the Siddiqi laboratory at UC Berkeley. Topics include simultaneous measurements of multiple non-commuting observables, the active use of the quantum Zeno effect with a moving measurement basis for qubit control, and subtle aspects about the information content contained in the collected stochastic readout.